Combine butter and basil. Set aside. Preheat grill to medium heat. Cut zucchini and yellow squash into thin slices. Slice portobello mushrooms. Slice red onions into thin circles. Remove stems and membranes from peppers. Flatten with palm of hand. Spray large grill pan with cooking spray. Arrange half the vegetables in a single layer on grill pan. Place grill pan on grill. Let cook 4-5 minutes then turn over and cook another 4-5 minutes. Repeat with second half of veggies.
While vegetables are cooking, combine cheeses in a medium bowl. Set aside.
When vegetables are cooked, remove from pan and add to a large bowl along with the pesto, salt, and pepper. Toss well to coat. Preheat griddle or large skillet. Spread the butter mixture in a thin layer on one side of one tortilla. Add, buttered-side down, to hot skillet. Top with 1/6 the veggies and 1/6 the cheese. Fold tortilla over so it's a half circle. Cook 2-3 minutes or until golden brown on the bottom. Carefully flip and cook an additional 2-3 minutes or until golden brown on second side. Remove from skillet and keep warm. Repeat with remaining ingredients.